Sufficient Conditions for a Josephson Inequality

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Abstract
An inequality dνf≥2−α is derived under conditions that are known to hold rigorously for Ising ferromagnets. Here d is dimensionality and ν and α are critical exponents expressed in customary notation, while f is a factor that is shown to be unity when 1≥α≥α′≥0, and in this case the inequality reduces to one proposed by Josephson. For 0<α<α′<1<δ, f is bounded from above to yield, in combination with the first result, dν≥(2−α) min1,1−2(α′−α)(δ−1)(2−α)(1−α′).